I don't know about open source or other free FPS games as most I've seen that were free were pretty crappy games (solely due to lack of resources during creation). That said games like Half-life and half-life 2 both can be modded for single player campaigns, I know I've downloaded single player mods for both of them. "They Hunger" comes to mind for half life, which was a zombie survival horror style fps single player mod for the original half life engine. I'm sure half life 2 can be modded similarly for single or multiplayer so those would be worth checking out. Valve is great about providing the community with user tools for creating user made content.
Past that, any game that is moddable and has a single player game probably allows for single player mods. The games may FOCUS on multiplayer themselves, but if they have any capacity for single player I'm sure that you could create a mod that has a larger single player scope then the developers chose to pursue. Multiplayer only games may be able to be modded into a single player excursion but you'd want to check specific games.
If you have limited experience I'd say stick with the big names, going with open source games would require actually knowing the coding languages involved as an open source game is unlikely to provide tools for easy game modifications. Also the bigger the game, and bigger the toolset, the bigger the community support will be and therefor you can find lots of help if you get stuck on the way.
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